Originally Posted by

**cmj1988** Yes, you completed my definition.

So I want to show that V(I) in R (which is the collection of prime ideals) gets sent to f*^(-1)(V(I)) such that V(f(I)) in S. Foote's notation is something I'm not use to. In this class our professor just goes off of his notes.

I'm still a bit shakey on how to prove this. I do understand your explanation though. If we invoke the rule we used in defining f*, we can see that f*^(-1)(V(I)) is f(V(I)) which is contained in some P in S.

I'm not sure if that works at all.

Btw, we have not been introduced to this Zariski topology stuff.